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The boy who knew too much: a child prodigy

This is the true story of scientific child prodigy, and former baby genius, Ainan Celeste Cawley, written by his father. It is the true story, too, of his gifted brothers and of all the Cawley family. I write also of child prodigy and genius in general: what it is, and how it is so often neglected in the modern world. As a society, we so often fail those we should most hope to see succeed: our gifted children and the gifted adults they become. Site Copyright: Valentine Cawley, 2006 +

Friday, July 06, 2012

The Higgs Boson discovery and clamouring to be wrong.


I noticed something interesting about the discovery of the Higgs Boson. It wasn’t the discovery itself, it was the reaction of physicists to that discovery that struck me. In particular, so many of the scientists clamoured to be wrong. I shall explain.

A number of physicists who were interviewed expressed the thought, in various ways, that they hoped that the Higgs Boson turned out to have properties INCONSISTENT with the STANDARD MODEL. That is, they were clamouring to be wrong. They wanted their existing theory to be overturned and be shown to be incorrect by the new discovery. Indeed, the famed Stephen Hawking had bet good money that the Higgs Boson would not be discovered – because he hoped that science would be proven wrong in its present models, because, I inferred, science is at its most interesting, when it is wrong-footed. It is in such times, that great advances in understanding are made. So, it is, that all these physicists want to be shown wrong. They want, in short, to usher in times of uncertainty and discovery and new thought and experiment and theory. They want intellectual excitement in their lives. Were the Higgs Boson to be proved to be exactly as expected then none of these things would happen. It would be business as usual. The world would continue much as it had before and they would have no surprises to wake up to each morning. The physicists didn’t want that. They wanted to live in revolutionary times. They were tired of stasis.

I rather feel that many branches of science will, in time, be filled with scientists thinking much like those physicists. As science matures and ignorance recedes, there will be the growing feeling that there is much less left to understand – that no big revolutions lie ahead. Thus, it is, that science will become less interesting for its practitioners. I cannot say if science has already reached that stage, but it is not difficult to feel that it cannot be far off for some branches of science, if it is not already here.

Scientists want to feel intellectually alive. To do so, they need times of change and challenge. Only, therefore, discovery that they were wrong, would usher in such times, assuredly. It would show them that they need to go back to the drawing board and begin again. Such a thought, does not tire them, but invigorates them. They wish to really live the life of the mind and to breathe its fresh thoughts.

In a way, I hope that the physicists get their wish – because times of change are exciting for the spectator, too – as I now am to that branch of science. Just to witness novel thoughts and theories, is a pleasure for those who appreciate matters of the mind. So, let us hope that the discovery of the Higgs Boson has some surprises for us. Let us hope it ushers in a new and deeper, richer, more complex understanding of the world – and with it brings us new powers over nature, that, I hope, we use wisely.

Just as the discovery of the electron ultimately led to electronics, perhaps the discovery of the Higgs Boson will lead to technologies of mass manipulation – which would obviously be both powerful and exciting in their applications: flying cities, anyone? The possibilities are as endless as our dreams. I shall watch the tale of the Higgs Boson with great anticipation – and so, too, I hope shall all Mankind. It could portend a very different world, indeed.

Posted by Valentine Cawley

(If you would like to support my continued writing of this blog and my ongoing campaign to raise awareness about giftedness and all issues pertaining to it, please donate, by clicking on the gold button to the left of the page.

To read about my fundraising campaign, please go to: http://scientific-child-prodigy.blogspot.com/2011/01/fundraising-drive-in-support-of-my.html and here: http://scientific-child-prodigy.blogspot.com/2011/01/fundraising-drive-first-donation.html

If you would like to read any of our scientific research papers, there are links to some of them, here: http://scientific-child-prodigy.blogspot.com/2011/02/research-papers-by-valentine-cawley-and.html

If you would like to see an online summary of my academic achievements to date, please go here: http://www.getcited.org/mbrz/11136175To learn more of Ainan Celeste Cawley, 10, or his gifted brothers, Fintan, 7 and Tiarnan, 5, please go to: http://scientific-child-prodigy.blogspot.com/2006/10/scientific-child-prodigy-guide.html

I also write of gifted education, child prodigy, child genius, adult genius, savant, megasavant, HELP University College, the Irish, the Malays, Singapore, Malaysia, IQ, intelligence and creativity.

There is a review of my blog, on the respected The Kindle Report here:http://thekindlereport.blogspot.com/2010/09/boy-who-knew-too-much-child-prodigy.html

Please have a read, if you would like a critic's view of this blog. Thanks.

You can get my blog on your Kindle, for easy reading, wherever you are, by going to: http://www.amazon.com/Boy-Who-Knew-Too-Much/dp/B0042P5LEE/ref=sr_1_1?ie=UTF8&m=AG56TWVU5XWC2&s=digital-text&qid=1284603792&sr=8-1

Please let all your fellow Kindlers know about my blog availability - and if you know my blog well enough, please be so kind as to write a thoughtful review of what you like about it. Thanks.

My Internet Movie Database listing is at:http://imdb.com/name/nm3438598/

Ainan's IMDB listing is at http://imdb.com/name/nm3305973/

Syahidah's IMDB listing is at http://imdb.com/name/nm3463926/

Our editing, proofreading and copywriting company, Genghis Can, is athttp://www.genghiscan.com/This blog is copyright Valentine Cawley. Unauthorized duplication is prohibited. Use only with permission. Thank you.) 

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Thursday, May 05, 2011

The company of peers.

Last week, I chanced upon a scene that had, about it, a quiet contentment.

I had gone to collect my son, Ainan, from HELP University College. I was running early and had a few minutes to wait before his class was to end. Curious, I peeked in to the classroom, partly to make sure I was waiting in the right place. The scene that I witnessed was one to bring comfort to any father, who had taken the particular path in raising his son that I had.

Ainan sat at a table, in this Physics class, with three other students. He was talking, naturally, to them, and they were listening. What struck me about it was how comfortable he seemed, in that situation: a boy of 11, conversing with young adult students, in a Physics class. It was not his comfort alone that was evident: it was the attitude of the other students – they fully accepted him, as a fellow student, on equal footing.

I saw, then, how right I had been to make this opportunity for him. He seemed so at home, in that class, with young adult students. He had found his place. It seems to me, looking back, that he is more at home, at HELP University College, than he was in primary school. In the latter situation, he always seemed to be holding his true essence in reserve, unable to share it with his fellow school kids, because they simply wouldn’t have understood. Now, however, I think he is able to speak more fully of his thoughts, for understanding is more readily achieved. In other words, he is freer now, than he was before, at least in the intellectual dimension. His playful side is expressed at home, with his siblings, and when he has the chance to mix with kids his own age. So, now, I rather think he has achieved a more complete life: one that allows him to express himself intellectually, one that affords him peers who can understand him – as well as the other aspects of childhood, which are still available to him.

I shall hold that memory of him, speaking in a very relaxed way, with his fellow students. It is an image of contentment that, at one time, I did worry we would never find for him.

All this does make me reflect on all the naysayers against educational acceleration. So many ill-informed educators feel that gifted children should never be accelerated. If only they knew how content Ainan was, with his University, compared to his primary school, they would realize how wrong they are. All they would have to do to realize this, is to peek through that window, and see what I saw, that day.

(If you would like to support my continued writing of this blog and my ongoing campaign to raise awareness about giftedness and all issues pertaining to it, please donate, by clicking on the gold button to the left of the page.

To read about my fundraising campaign, please go to: http://scientific-child-prodigy.blogspot.com/2011/01/fundraising-drive-in-support-of-my.html
and here: http://scientific-child-prodigy.blogspot.com/2011/01/fundraising-drive-first-donation.html

If you would like to read any of our scientific research papers, there are links to some of them, here: http://scientific-child-prodigy.blogspot.com/2011/02/research-papers-by-valentine-cawley-and.html

If you would like to see an online summary of my academic achievements to date, please go here: http://www.getcited.org/mbrz/11136175

To learn more of Ainan Celeste Cawley, 10, or his gifted brothers, Fintan, 7 and Tiarnan, 5, please go to: http://scientific-child-prodigy.blogspot.com/2006/10/scientific-child-prodigy-guide.html

I also write of gifted education, child prodigy, child genius, adult genius, savant, megasavant, HELP University College, the Irish, the Malays, Singapore, Malaysia, IQ, intelligence and creativity.

There is a review of my blog, on the respected The Kindle Report here: http://thekindlereport.blogspot.com/2010/09/boy-who-knew-too-much-child-prodigy.html

Please have a read, if you would like a critic's view of this blog. Thanks. You can get my blog on your Kindle, for easy reading, wherever you are, by going to: http://www.amazon.com/Boy-Who-Knew-Too-Much/dp/B0042P5LEE/ref=sr_1_1?ie=UTF8&m=AG56TWVU5XWC2&s=digital-text&qid=1284603792&sr=8-1

Please let all your fellow Kindlers know about my blog availability - and if you know my blog well enough, please be so kind as to write a thoughtful review of what you like about it. Thanks.

My Internet Movie Database listing is at: http://imdb.com/name/nm3438598/

Ainan's IMDB listing is at http://imdb.com/name/nm3305973/

Syahidah's IMDB listing is at http://imdb.com/name/nm3463926/

Our editing, proofreading and copywriting company, Genghis Can, is at http://www.genghiscan.com/

This blog is copyright Valentine Cawley. Unauthorized duplication is prohibited. Use only with permission. Thank you.)

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Tuesday, March 29, 2011

My favourite Einstein story.

A Berlin music critic in the early 1920s listened to a violin performance, by Albert Einstein. Afterwards, he gave his assessment:

"Einstein's playing is excellent, but he does not deserve his world fame - there are many others just as good."

The critic was unaware that Einstein's fame was founded in Physics, not music!

(If you would like to support my continued writing of this blog and my ongoing campaign to raise awareness about giftedness and all issues pertaining to it, please donate, by clicking on the gold button to the left of the page. To read about my fundraising campaign, please go to: http://scientific-child-prodigy.blogspot.com/2011/01/fundraising-drive-in-support-of-my.html and here: http://scientific-child-prodigy.blogspot.com/2011/01/fundraising-drive-first-donation.html

If you would like to read any of our scientific research papers, there are links to some of them, here: http://scientific-child-prodigy.blogspot.com/2011/02/research-papers-by-valentine-cawley-and.html

If you would like to see an online summary of my academic achievements to date, please go here: http://www.getcited.org/mbrz/11136175

To learn more of Ainan Celeste Cawley, 10, or his gifted brothers, Fintan, 7 and Tiarnan, 4, this month, please go to: http://scientific-child-prodigy.blogspot.com/2006/10/scientific-child-prodigy-guide.html

I also write of gifted education, child prodigy, child genius, adult genius, savant, megasavant, HELP University College, the Irish, the Malays, Singapore, Malaysia, IQ, intelligence and creativity.

There is a review of my blog, on the respected The Kindle Report here: http://thekindlereport.blogspot.com/2010/09/boy-who-knew-too-much-child-prodigy.html

Please have a read, if you would like a critic's view of this blog. Thanks.

You can get my blog on your Kindle, for easy reading, wherever you are, by going to: http://www.amazon.com/Boy-Who-Knew-Too-Much/dp/B0042P5LEE/ref=sr_1_1?ie=UTF8&m=AG56TWVU5XWC2&s=digital-text&qid=1284603792&sr=8-1

Please let all your fellow Kindlers know about my blog availability - and if you know my blog well enough, please be so kind as to write a thoughtful review of what you like about it. Thanks.

My Internet Movie Database listing is at: http://imdb.com/name/nm3438598/

Ainan's IMDB listing is at http://imdb.com/name/nm3305973/

Syahidah's IMDB listing is at http://imdb.com/name/nm3463926/

Our editing, proofreading and copywriting company, Genghis Can, is at http://www.genghiscan.com/

This blog is copyright Valentine Cawley. Unauthorized duplication is prohibited. Use only with permission. Thank you.)

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Monday, January 04, 2010

HELP University College, KL, Malaysia.

It is time to announce it. Ainan has joined HELP University College, in Kuala Lumpur, Malaysia.

We spent the last three years trying to secure the right educational opportunities for Ainan, in Singapore. However, it wasn't easy. The "system" was very difficult to work with. It took us, for instance, about 22 months to secure consistent practical Chemistry classes for him, in Singapore, at a Polytechnic there, (which we much appreciate and which helped, at the time. Sadly, though, it wasn't really enough.). That is almost two years completely wasted...two years of frustration, of being stalled, of being thwarted. It is not as if we didn't try to get what he needed in Singapore. We did. However, the system was most modest in its response. The GEP (Gifted Education Programme) arranged for a handful of practical Chemistry classes for him - which we were very grateful for, at the time - but it never led anywhere. There was no ongoing practical Chemistry provision made available for him. We were, at the time, given two excuses for this: "There are no resources available" and "If we do it for him, they will all want it."

The funny thing is, it was never clear who the "they" were, since, in Singapore's history, to date, there has only been one child like Ainan. Presumably, providing Ainan with lab access would suddenly have turned the whole nation into science prodigies by a kind of infective osmosis. How ridiculous.

Anyway, we tried everything we could in Singapore. We even asked to homeschool him, on many occasions, but permission was never granted. (We were always fobbed off with "We will revert to you shortly"...and then we would never hear from them - the Compulsory Education Unit - again.). After three years of it, we quietly gave up and started looking elsewhere for an education for Ainan.

Remarkably, Malaysia proved very responsive - and, through the wise advice of Zuhairah Ali, President of the National Association of Gifted Children of Malaysia - Ainan secured places at University Colleges in Malaysia, in a very short time...not much more than a week.

Of all the places on offer, we chose HELP University College, in Kuala Lumpur. It offered the best overall support of Ainan.

At HELP, Ainan will be taking an American Degree Programme - starting immediately. He will take Computer Science options, but also keep up his Chemistry. He will, in addition, be broadening his science foundation by adding A levels in Physics and Maths to his tally, simultaneously. He already has AS Level Chemistry, O level Chemistry and O level Physics, as well as having taught himself some degree of programming skills.

Our thanks to HELP for offering him a place and being so supportive - and to Zuhairah Ali for her speed, efficiency and immense resourcefulness. Thank you.

(If you would like to learn more of Ainan Celeste Cawley, a scientific child prodigy, aged eight years and seven months, or his gifted brothers, Fintan, five years exactly, and Tiarnan, twenty-eight months, please go to:http://scientific-child-prodigy.blogspot.com/2006/10/scientific-child-prodigy-guide.html I also write of gifted education, IQ, intelligence, the Irish, the Malays, Singapore, College, University, Chemistry, Science, genetics, left-handedness, precocity, child prodigy, child genius, baby genius, adult genius, savant, wunderkind, wonderkind, genio, гений ребенок prodigy, genie, μεγαλοφυία θαύμα παιδιών, bambino, kind.

We are the founders of Genghis Can, a copywriting, editing and proofreading agency, that handles all kinds of work, including technical and scientific material. If you need such services, or know someone who does, please go to: http://www.genghiscan.com/ Thanks.

IMDB is the Internet Movie Database for film and tv professionals. If you would like to look at my IMDb listing for which another fifteen credits are to be uploaded, (which will probably take several months before they are accepted) please go to: http://www.imdb.com/name/nm3438598/ As I write, the listing is new and brief - however, by the time you read this it might have a dozen or a score of credits...so please do take a look. My son, Ainan Celeste Cawley, also has an IMDb listing. His is found at: http://www.imdb.com/name/nm3305973/ My wife, Syahidah Osman Cawley, has a listing as well. Hers is found at: http://www.imdb.com/name/nm3463926/

This blog is copyright Valentine Cawley. Unauthorized duplication prohibited. Use Only with Permission. Thank you.)

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Thursday, February 05, 2009

Science is harder than the Arts.

A recent study has proven what has long seemed obvious to anyone who has ever observed pupils in school: Sciences are harder than the Arts.

The study, at Durham University examined the examination results of over a million students and was commissioned by the Institute of Physics and SCORE (Science Community Representing Education).

Students of similar ability, but different subject choice were compared to extract the relative hardness of subjects. The core finding was that science subjects at A level were a grade harder than Arts subjects, in general. This means that a student will score lower on a Science subject, than an Arts subject, although be of the same intellectual standard. Indeed, those behind the study commented that: "A student who gets a C in Biology is going to be generally more able than a student who gets a B in Sociology."

Differences were noted within the Arts subjects, too, with some being demonstrably easier than others. A student studying film studies instead of History can expect more than a grade improvement in his or her results. A student picking media studies instead of English, improves by half a grade.

Students seem to be aware of this. There is a long-term decline in the number of students studying the harder science subjects - and a long-term rise in the number of students picking soft subjects. Since the mid-90s, the proportion of students taking media, film and tv studies has risen by over 250 per cent; while the proportion taking Physical Education and Psychology has doubled. Meanwhile, such subjects as Physics and Chemistry have slipped.

Now, I find this very strange. It seems that examining boards are not standardizing the grading across subjects. All that is necessary to correct for this is to ensure that a student of known ability would perform at the same grade across all subjects, assuming equal effort in each. An A grade in Film Studies, should be just as hard to get as an A grade in Physics. If it isn't, then more credit should be given to students who study harder subjects. Either the exam grading systems must change to reflect these inherent differences in ease of subject - or the way exams are regarded by Universities should change.

Indeed, there are signs that Universities are making moves in the right direction. Both Cambridge University and the London School of Economics have published a list of subjects that they consider too easy = and indicated that they will not accept anyone who studies more than one of them, out of their subject offering.

If it is indeed so, that a Biologist with a C is better than a Sociologist with a B, then Universities should begin to decline Sociologists with a B in preference for Biologists with a C. Perhaps then their student body will begin to reflect the best of the applicants, rather than the most adept at choosing cushy subjects.

I don't know if it was just my school, or not, but this phenomenon was easily observable among the students there. The pupils of exclusively Arts subjects were generally less bright than the students of Science subjects. It didn't take a large study to see this: it was immediately evident.

My question is: is this a global phenomenon? Is it just UK exams that reflect this bias, with Science exams being inherently tougher than Arts exams? How about your country? Do you think Arts students seem less bright than Science students? Are Arts exams easier?

Comments please.

(If you would like to learn more of Ainan Celeste Cawley, a scientific child prodigy, aged eight years and seven months, or his gifted brothers, Fintan, five years exactly, and Tiarnan, twenty-eight months, please go to: http://scientific-child-prodigy.blogspot.com/2006/10/scientific-child-prodigy-guide.html I also write of gifted education, IQ, intelligence, the Irish, the Malays, Singapore, College, University, Chemistry, Science, genetics, left-handedness, precocity, child prodigy, child genius, baby genius, adult genius, savant, wunderkind, wonderkind, genio, гений ребенок prodigy, genie, μεγαλοφυία θαύμα παιδιών, bambino, kind.

We are the founders of Genghis Can, a copywriting, editing and proofreading agency, that handles all kinds of work, including technical and scientific material. If you need such services, or know someone who does, please go to: http://www.genghiscan.com/ Thanks.

This blog is copyright Valentine Cawley. Unauthorized duplication prohibited. Use Only with Permission. Thank you.)

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posted by Valentine Cawley @ 4:32 PM  13 comments

Saturday, May 17, 2008

I am not a Chemist.

The headline is an important statement that must be understood, if Ainan is to be understood.

It has come to my attention that some people assume that Ainan's interest is an echo of my own. I have had people assume that I am, in fact, a Chemist - and that Ainan's pursuit of the subject is just him either aping his Daddy or being indoctrinated by him. Neither proposal is true. Ainan chose Chemistry, it was not chosen for him.

When I was very young I, too, was interested in Chemistry. Yet, I didn't introduce Ainan to it. It never occurred to me to do so. Ainan introduced himself to Chemistry. He taught himself at first, without any influence from either of his parents. In recent months, he has begun looking at other sciences, too. This, again, is his doing - a need to explore more widely, as well as deeply (for he continues to explore Chemistry). Again, it is Ainan that is leading - he is the one who lays down his own fields of interest and begins to address them.

I was a type of scientist once - a physicist. So, if I were forming Ainan's interests it would be to that subject I would have led him. I certainly would not have led him to a subject other than my own prior core interest.

So, Ainan is a Chemist because he wants to be one. Ainan is exploring other sciences, now (including Physics) because he wants to explore them. Ainan is his own path-chooser.

I address this issue because I was surprised to learn that even relatives of mine made the assumption that Ainan was doing what I wanted, rather than what he wanted. Frankly, I was surprised at that for many reasons - not least of which is that I think it is impossible for a child to perform at a high level in an externally chosen area. They would not have the drive to mastery if it was imposed from without: their own curiosity must be the guiding force.

(If you would like to learn more of Ainan Celeste Cawley, a scientific child prodigy, aged eight years and five months, or his gifted brothers, Fintan, four years and ten months, and Tiarnan, twenty-seven months, please go to: http://scientific-child-prodigy.blogspot.com/2006/10/scientific-child-prodigy-guide.html I also write of gifted education, IQ, intelligence, the Irish, the Malays, Singapore, College, University, Chemistry, Science, genetics, left-handedness, precocity, child prodigy, child genius, baby genius, adult genius, savant, wunderkind, wonderkind, genio, гений ребенок prodigy, genie, μεγαλοφυία θαύμα παιδιών, bambino, kind, niño, gênio criança, gifted adults and gifted children in general. Thanks.)

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posted by Valentine Cawley @ 9:00 PM  3 comments

Thursday, November 08, 2007

A Global Search for a University

We are looking for a University for Ainan because he will soon have taken A level - and once he has done that, he would need further opportunity to study - otherwise he would stagnate.

A level is at the level of a Major in an American Bachelor's degree. Ainan is ready to do that soon. But what will he do then? We have nothing in place at present, so we have to line something up for him. We are, therefore, interested in hearing from any University, worldwide that offers Chemistry and other sciences.

Our needs are quite specific, but a University need not meet all of our needs to be acceptable. Firstly, the University must have a strong Chemistry department. Then they should offer a wide spectrum of other sciences especially Physics, Material Sciences, Geology and Astronomy, as well as, ideally, Nanotechnology and Biology. These are secondary interests.

The medium of instruction should be English. The culture should be warm, accepting and welcoming. It should be a supportive, co-operative environment. Too many Universities are overly competitive, aggressive and hostile environments (in my view). That would not suit Ainan.

The University should be prepared to offer mentors. He is young and their guidance would be helpful. It should also be located in a relatively safe place. We don't want to have to worry about such things, unduly.

We are prepared to look anywhere in the world that is a reasonably comfortable place to live. As long as the University can provide a nurturing environment we would be interested in hearing from them.

If you are with a suitable University, or know of any, please contact us and tell us the details. We will then correspond to see if anything can be worked out.

Your help in this is very much appreciated. Thanks.

(If you would like to learn more of Ainan Celeste Cawley, a scientific child prodigy, aged seven years and eleven months, or his gifted brothers, Fintan, four years and four months, and Tiarnan, twenty-one months, please go to: http://scientific-child-prodigy.blogspot.com/2006/10/scientific-child-prodigy-guide.html I also write of gifted education, IQ, intelligence, the Irish, the Malays, College, University, Chemistry, Science, genetics, left-handedness, precocity, child prodigy, child genius, baby genius, adult genius, savant, gifted adults and gifted children in general. Thanks.)

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posted by Valentine Cawley @ 12:24 AM  6 comments

Monday, June 11, 2007

Johann Carl Friedrich Gauss

Some of history's greatest thinkers began life as child prodigies. What is interesting, to me, is that not everyone seems to know this.

Johann Carl Friedrich Gauss was a classic and remarkable case of child prodigy, emerging from an unpromising background. He was born on the 30th April 1777 in Brunswick, Germany. Neither of his parents were educated - indeed, his father was a stone mason. So, the young Gauss was very much on his own, in his early education. Yet, he was not without success. By the age of three he had somehow taught himself reading and arithmetic to a proficient degree.

One day, his father was adding up some figures, on paper, concerning the family finances. The young Gauss, three, peered over at his father's work and pointed out an arithmetical error - which Gauss had checked in his head.

In time, Gauss came to the attention of the Duke of Brunswick and, as was the custom of the day - and a good custom it was too - Gauss was to receive the patronage and support of the Duke of Brunswick, throughout much of his career. The Duke awarded Gauss a fellowship to the Collegium Carolinum, which he attended from 1792 to 1795 and thence he went to the University of Gottingen, which he attended from 1795 to 1798.

It was while at the University that Gauss began the train of mathematical breakthroughs that were to characterize his work and life. In 1796, he proved that any polygon with a number of sides equal to a Fermat prime may be constructed with a compass and straightedge. This was a major mathematical discovery since the problem of construction of such shapes had bedevilled mathematicians since the Ancient Greeks. It took the young Gauss to finally solve it.

Admission to University seems to have electrified Gauss into creative action. The construction problem was solved on March 30, 1796. A few days later, on April 8th, he proved the Quadratic Reciprocity law, which allowed one to determine the solvability of any quadratic function in modular arithmetic.

Modular arithmetic? Oh, he invented that, too. Then he came up with the Prime Number Theorem about the distribution of primes amongst all integers, on May 31st. On July 1oth he discovered that any positive integer is the sum of, at most, three triangular numbers. On October 1st, he published some work on the number of solutions of polynomials with coefficients in finite fields.

This outburst of creativity was not a solitary occurrence in Gauss' life. He went on to make lifelong contributions in many fields. I wrote in detail of that one year to give you some idea of what he was capable of. In 1799, he proved the fundamental theorem of algebra. In 1801, he published his book on number theory, Disquisitiones Arithmeticae, a magnum opus which he had actually completed at the age of 21, though he delayed publishing (this was a chronic tendency of his, failing to publish until, in his perfectionism, he was satisfied with his work. Had he published all that was later to be found in his notebooks, it is estimated that he would have advanced mathematics fifty years, single-handedly. However, in delaying publication, other mathematicians often got to publish Gaussian results before he did, though he had reached the same conclusions decades ahead of them).

In that same year, 1801, Giuseppe Piazzi discovered the planetoid Ceres. He tracked it for a few months, across three degrees of sky, but was unable to locate it again. (It had been lost behind the glare of the sun.) The astronomers of the time were unable to calculate an orbit sufficiently well on so little information to be able to predict the path of an object. Gauss, however, just 23 at the time, took on the project. In three months of work, he revolutionized how orbital calculations were performed, devising an approach which still stands as the foundation of such calculations today. He accurately stated where the object could be expected to be seen in the night sky - and Ceres was duly found again. This single piece of work catapulted Gauss to fame - and was later key in securing him the lifelong position of astronomer at Gottingen.

Gauss' achievement with Ceres puzzled many, for it seemed a feat beyond possibility. He was asked how he had done such an intricate calculation. He replied: "I used logarithms." When asked how he had looked up so many logarithms in so short a time, he dumbfounded them, by saying: "Who needs to look them up? I calculated them in my head."

Thus Gauss carried into his adult life the childhood ability as a mental calculator that he had shown at the age of three.

Gauss put his mental calculation to another practical use through performing a geodesic survey of the state of Hanover. In so doing, he developed what we know today as the Normal Distribution - or more properly, Gaussian distribution.

In the 1820s he collaborated with the physicist Wilhelm Weber and contributed much to the areas of optics, acoustics, mechanics and magnetism. Indeed, in 1833 he invented the telegraph, which was to later revolutionize communications that century.

Subsequent to his death on February 23rd, 1855, his brain was taken from his skull and weighed. It was, perhaps not surprisingly, significantly heavier than usual, at 1,492 grams and, the examiner stated that it was "highly and deeply convoluted". It was theorized that this unusual manifestation of the brain accounted for his genius.

Johann Carl Friedrich Gauss, began life as a self-educated child prodigy, born of uneducated parents, who could not, therefore, assist him but, by the end of his days, he was accounted, by many, as "the greatest mathematician since antiquity".

(If you would like to read about Ainan Celeste Cawley, seven years and six months, a scientific child prodigy, or his gifted brothers, Fintan, three, or Tiarnan, sixteen months, please go to: http://scientific-child-prodigy.blogspot.com/2006/10/scientific-child-prodigy-guide.html I also write of gifted education, IQ, intelligence, child prodigy, child genius, baby genius, adult genius, savant, the creatively gifted, gifted children and gifted adults in general. Thanks.)

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posted by Valentine Cawley @ 3:26 PM  12 comments

Tuesday, June 05, 2007

Child prodigies and Nobel Prizes

Do child prodigies grow up to be Nobel Prize Winners? I ask this because it is clear that some people believe that child prodigies don't or won't do any such thing. (I can tell from the content of the searches with which they arrive on my site.) There is a general lack of awareness of what child prodigies have actually gone on to do, as adults. Perhaps this is because there is often more attention focussed on their childhoods than on their later adult achievements - or if they achieve big things, there is a tendency to focus on their adult achievements and forget their childhoods. Either way, there is a kind of reporting bias that obscures the truth of the lives child prodigies. Many of them go on to do interesting things.

One example is Lev Landau. Now, if you are of a certain age, you would recognize his name. He was a Physicist, born on January 22nd, 1908 into a Jewish family based in Baku, Azerbajian. He had a most curious childhood and was very early recognized as a child prodigy in mathematics - indeed, so early did he develop this gift that, he was later to say of his childhood: "I can't remember a time when I wasn't familiar with calculus."

This promising beginning bore fruit and he graduated from the Gymnasium at 13, but was not allowed to go immediately to University so he entered Baku Economical Technical School at 13. A year later, at 14, he matriculated at Baku University, in 1922, studying in two departments simultaneously - the Physico-Mathematical and the Chemistry departments. In 1924 he moved to the Leningrad University, graduating in 1927, and then to the Leningrad Physico-Technical Institute, from which he received his doctorate at the age of 21.

In his early career, he managed to study for a time at the Niels' Bohr Institute of Theoretical Physics in Copenhagen - a time which was seminal for him. On his return to the Soviet Union, he began to publish a stream of papers in Theoretical Physics. His greatest contribution was the Theory of Superfluidity in which he explained the properties of liquid helium, but he also wrote many papers across the fields of Physics: discovering the density matrix method in quantum mechanics, the Ginzburg-Landau Theory of Superconductivity, the quantum theory of diamagnetism, the theory of second-order phase transitions, Landau damping in Plasma Physics, the Landau pole in quantum electrodynamics, and the two-component theory of neutrinos.

In 1962, for his work on Superfluidity, Lev Landau received the Nobel Prize in Physics. This was also the year he was involved in a head-on collision with a truck, on January 7. He spent three months in a coma and was never to recover his creative abilities. He died on April 1st, 1968, as a consequence of the injuries he sustained.

Lev Landau is one of many child prodigies in history who grew up to be as distinguished as an adult as he had been as a child. He received many prizes in his lifetime for his diverse work - including the Max Planck Medal, the Fritz London Prize, the U.S.S.R State Prize (which he was awarded several times) and the Lenin Science Prize. It is, however, the most famous prize of all, the Nobel Prize, that we tend to remember.

He was a foreign member of both the Royal Society, London and a Foreign Associate of the American Academy of Sciences of the USA among many other international societies.

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posted by Valentine Cawley @ 6:22 AM  0 comments

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